wood peeling with a knife and curling its chips
An opportunity to test the 2.91 boolean modifier options...

There are two rods in the scene (a copy of the first one but different material), one for what we see as the rod and another for the cut.
The first one has a boolean modifier set to &quot;exact&quot;:

The second a boolean and a simple deform (&quot;bend&quot;) modifier driven by the empty (which is parented to the cube). But here the boolean is set to &quot;fast&quot; because if the shape is plain, simple deform will transform it badly.
The cutting cube is parent of an empty that is used as pivot point for the bending.